The spectral complexity Cs assigns an information cost proportional to the dominant wavenumber of the fermionic wavefunction. Under Solomonoff induction, P(ψ) ∝ 2−Cs(ψ), so a genuine mass-from-complexity relation would order observable fermions by ascending Cs.
The (n,m) classification of Section 5 does not yet support this. All three charged leptons — electron, muon, tau — occupy the same class, (n,m) = (2,1). The classification distinguishes charge and confinement (m as winding number, n as site count) but contains no third parameter that could distinguish particles of different mass within a class. A genuine derivation of the lepton mass hierarchy from Cs therefore requires extending the classification with an explicit generation index, which does not yet exist in this framework.
| Fermion | Mass (MeV) | log 2(m∕me) | Notes |
| Electron | 0.511 | 0.00 | |
| Muon | 105.66 | 7.69 | |
| Tau | 1776.86 | 11.76 |
A combinatorial argument is sometimes proposed as a candidate origin for a discrete mass unit: one fermion hop requires four binary choices (which site, which frame, real or imaginary component, sign of phase), giving 24 = 16 configurations and suggesting a 4-bit granularity. This argument is independently motivated but is not connected by any derivation to the Cs formula of Paper VI or to the observed mass gaps in Table 3. No construction in this framework takes (n,m) = (2,1) together with a generation label and outputs Cs = 8 or Cs = 12. The near-integer appearance of 7.69 → 8 relies on rounding a number that is not itself derived, and the second gap (4.07) is not close to the same unit that the first gap is rounded to.
We therefore do not claim a mass ladder. The honest status is: the (n,m) classification correctly separates fermions by charge and confinement class, but says nothing yet about why three charged-lepton masses exist within the single class (2,1), or what values they should take. This is stated as an open problem in Section 12 rather than as a partial result.